As illustrated in FIGS. 1-4, a prior art expandable handle of the luggage is composed of two outer tubes 11 fastened with a shell of the luggage, and two joint members 12. The joint members 12 are made up of a housing 13, a rotary member 14 provided with two locating slots 141 and 142, a guide rod 15, and a spring 16 fitted over the guide rod 15, a locating member 17 provided with a projection 171 which is urged by the spring 16. Two inner tubes 18 are received in the outer tubes 11 via the two rotary members 14. A handle 19 is fastened with the inner tubes 18. The inner tubes 18 can be first pulled out of the outer tubes 11 by the handle 19 and can be then forced by the handle 19 to form a predetermined angle with the outer tubes 11, as shown in FIGS. 3 and 4. The prior art handle described above is not versatile in function.